Engineers often need to be able to estimate or predict the real-world dynamic environment in which a device or component will operate in, so that so that an engineer can design and test the device or component for reliable operation in that environment. For example, electrical engineers may need to estimate the maximum electromagnetic wavefield strength in which an electronic component, device, or system must operate, so that they can design and test for immunity to electromagnetic interference. When electronics are housed within an enclosure, the electromagnetic field within the enclosure will become reverberant at higher frequencies (e.g., based on the wavelength relative to the dimensions of the enclosure), at which point electromagnetic wave reflections accumulate to create a multi-modal, reverberant response usually quantified by the total wavefield energy level. The reverberant energy level can typically only be quantified statistically because either the excitation is random or uncertain or because the exact modal parameters of the enclosure (which are dictated by the enclosure's dimensions and electromagnetic properties) are uncertain.
As another example, in the field of vibro-acoustics, engineers may need to estimate the maximum vibration level that sensitive equipment and/or payloads will experience during operation. For example, mechanical engineers designing a rocket or launch vehicle need to be able to estimate the maximum vibration level that is likely to be experienced in transonic flight, so that they can design and test for safe operation of the equipment in flight. The vibration wavefield response of the structural panels of the vehicle may be driven by unsteady aerodynamics forces during transonic flight. Again, the vibrational waves in the vehicle structural panel subsystems will reflect and scatter at higher frequencies, at which point the vibrations accumulate to create a reverberant vibrational energy level.
While various statistical energy analysis methods exist and can be employed to estimate the mean or average reverberant energy level, care must be taken so as not to underestimate the statistical variance about the mean, and the resulting maximum expected reverberant energy level, as any gross under estimation of maximum expected response at the design stage will lead to equipment failures in the operating environment. At the same time, any gross overestimate of the reverberant energy level can make it cost prohibitive to design devices or components for the estimated reverberant energy level. Accordingly, it is desirable to calculate or otherwise estimate the reverberant energy level in an accurate and reliable manner without grossly overestimating or underestimating the expected reverberant energy level.